Arousing My Albedo

Peg: ‘It WOULD be nice to give GWB a plug for something he did quite well. I’m talking about his home that is conservation in action. Here is a link to the snopes post about it.’

☞ Kudos to him for his energy-efficient Crawford house. The reader may supply his or her own devastatingly caustic follow-on line.

TRIANA’S MEDS

Clare D.: ‘Triana mentions Procrit and Advair. There is a generic for Advair. There is not one for Procrit, but it’s a relatively new drug which has to be injected. I’d be curious if appeals could not be made to the manufacturer for mercy dosage. I would hope that any med bill would include some way for people to easily check for themselves, the generics and the efficacy of various new drugs. Relying on doctors to do so is foolish in this day and age; doctors are encouraged to prescribe expensive drugs. Even doctors at Kaiser Permanente, I’m sure. Drug companies try to fool you: Caduet is the (more expensive, in-patent) version of Lipitor plus Norvasc. Norvasc has a generic equivalent and Lipitor has a similar generic, non-equivalent. Arthrotec is two generics combined into a non-generic one, the better to charge you more. With age, I’ve gone from essentially no pills to many for me and equally as many for my demented husband. Since I’m NOT demented, I have to keep track of them for both of us and stay as far short of the donut hole as possible. I have to be constantly on guard. Not all doctors are interested in saving money for their patients and frequently they just don’t KNOW the costs! I’ve learned that a lot of times the people who want to keep their aged parents on expensive drugs, at the expense of anyone BUT themselves, are people who have trouble with the idea of parents dying.’

☞ Leaving aside that most people have trouble with the idea of their parents’ dying, there’s a lot to what Clare says.

WHITE DRIVEWAYS

Worried about your carbon footprint? Instead of buying a new, more fuel efficient car for $30,000, you might consider buying a case of ‘striping spray paint‘ for $56. In the first place, you save the cost to the environment of MAKING a new car (you think energy and chemicals and carbon emissions don’t go into THAT?). And in the second, by my calculations, in this example, you save $29,944.

I got this idea from my old pal Richard Factor, who got it from thinking about the carbon footprint of his Prius. Even a Prius sends CO2 into the air. He says you should paint your driveway white.

‘Making roads and roofs a paler color could have the equivalent effect of taking every car in the world off the road for 11 years,’ Energy Secretary Steven Chu has said.

And really, that pretty well sums up the concept, for us laymen. White stuff reflects radiation, black stuff absorbs it. Whether you’re a guy out in the desert or a little planet called Earth, white is the cooler of choice.

You could stop reading there, but Richard summarizes his lengthier, calculation-ridden article here:

If you like to drive, or, for that matter, breathe, you may find it difficult to reduce your CO2 output. I cut mine in half, at least as far as driving is concerned, by buying a Prius hybrid. But still it’s only in half. What if I’m a serious believer in the threat, and want to reduce it to zero? No problem! There are organizations that sell ‘offsets.’ While most human activities create more carbon dioxide, some reduce it. Planting trees, increasing energy efficiency, ‘sequestering’ CO2 underground – all reduce its atmospheric burden. These organizations accomplish it in various ways. You accomplish it by – surprise! – sending them money.

Why Did The Chicken Cross the Road?

The road, in this case, is the kind of road you are likely to find in front of your house. It’s two lanes, separated by a yellow or double-yellow line down the center and two white “fog lines” demarking its edges. It’s paved with asphalt, often called “black top” because — let’s not always see the same hands — it’s black. The chicken crossed because once he stepped on it his feet got very hot, and, even with a brief respite gained by pausing at the yellow lines, he wanted to get to the other side and cool them off. Clever chicken! I made the same discovery one day when the shoe police were unaccountably preoccupied and thought to myself “If they made roads like this in ‘inverse video’ there would be a lot less heat absorbed by the planet.”

A quick Google search located a carbon footprint calculator, which in turn yielded the amount of money I would have to spend to compensate for the CO2 spewing forth from my Prius every year. It was about $45. I would have sent them a check right away, but that would mean they’d have 45 of my dollars and I wouldn’t. Instead I thought of an experiment. The global warming problem is (allegedly) occurring because CO2, a major culprit in the greenhouse effect, is causing solar radiation that would otherwise escape back into space to remain here and warm the planet. How about if I were to keep the $45, and instead put a mirror someplace where it would send that nasty radiation back to the sun? Although I don’t have a mirror, and may not have any good place to put it without complaints about the glare, I can at least think about it, right?

How much CO2 does my Prius emit on an annual basis? Easy! I know I used 425.2 gallons of gas during calendar 2006, thanks to my trusty spreadsheet. At 19.4 pounds per gallon, that’s 4.12 tons of carbon dioxide.

How much energy have I gotten from this gas? Each gallon contains 121MJ (Megajoule or million watt-seconds) which is the equivalent of 121,000,000/(3600*1000) = 33.6 kilowatt hours. (Although I haven’t “gotten” all this energy to move my car, one way or the other it has been added to the environment.) Thus, to make my car “energy neutral,” I have to somehow compensate for those tons of carbon dioxideand, although it is rarely mentioned as a problem, the energy I have added to the environment as well.

I was about to perform a long calculation here about how much energy the sun deposits on the earth, but I was saved the trouble. Quoting from the source:

Solar power per m2 on U.S. surface … this seems a little low … it’s 1342 watts per m2 outside the atmosphere, about 1000 watts per m2 at high noon on the ground, and on average (day and night) about 240 watts per meter2 absorbed at the ground. This is the average over the Earth too.

I’m going to assume that “absorbed at the ground” implies an albedo (reflectance) of zero. I’m also going to assume that 240 watt figure is correct for my location: At the equator it would be higher, at the poles it would be lower. At mid-latitude, it’s probably close enough. If I want to get rid of the energy I have added to the earth’s environment, all I have to do is radiate 452.2*33.6kWh of energy back into space. This is 15,194kWh and there are 8,760 hours in a year. Although I can’t redo the roads in inverse video, I can dump 240 watt-hours per hour per square meter back into space by putting a mirror over a black spot on my own driveway. I calculate that a mirror of about 20.6 square metres, or 14.7 feet on a side would be sufficient.

Mirrors and Albedo

After estimating the mirror size I realize that it’s not entirely practical. Not that I can’t find a 14.7 foot square spot to put it, but rather that I would have to send money to somebody else to get the mirror. But all is not lost! A clean mirror will have an albedo as close to 1 as matters. “Worn asphalt” as is present on my driveway and many others, has an albedo of .12. It seems entirely possible to achieve the albedo of “fresh snow” (.8-.9) artificially. Striping paint should do the job, and on a driveway it will get little wear and so stay clean and reflective. Re-estimating how much area would need to be raised from an albedo of .12 to .8 instead of the hypothetical effectiveness of the mirror (from 0 to 1), I come up with about 30 square meters instead of 20. I took a quick look at eBay (pay list for striping paint? Are you nuts?) and found that at least one seller had spray cans available, six for $15. These would be enough to cover almost 40 square meters, so if one has the space, clearly the cost isn’t prohibitive. So far so good.

But this isn’t the whole story. Striping the 30 square meters “remediates” the energy used driving the car. What about the accumulation of carbon dioxide?

The CO2 Question

Unlike the heat created by burning gasoline, CO2 doesn’t create heat at all. Rather, it can be viewed as amplifying sunlight. Instead of warming the earth directly, it allows the sun to warm the earth more than it otherwise would by preventing infrared radiation from escaping into space. Where does this infrared radiation come from? The sun emits radiation, both infrared and visible. Much of this energy is contained in the visible range. The visible light is converted to infrared when it is absorbed. In principle, therefore, painting more of the driveway white, which will reflect the visible light and hence energy into space, will reduce the amount of infrared that is available to be absorbed.

There is a conceptual problem with this, however. Painting a fixed portion of the driveway compensates for the annual component of the car’s energy use. As long as I continue to commute, that white patch I hypothetically painted a few paragraphs ago will remediate my heating the planet. However, the CO2 production is cumulative. Every year I add more to the atmosphere. While there are various (complicated) processes of equilibration, they typically exceed the life of the car and perhaps the life of the human driving it. Therefore, I would have to add more white paint every year to compensate for the cumulative addition of carbon dioxide to the atmosphere. Will I run out of driveway before I die?

Energy Balance

Unlike the energy-reflection calculation which is theoretically simple, calculating how much energy I have to reflect to compensate for that added by my 4.12 annual tons of CO2 is fraught with uncertainty. There are already a number of IR-absorbing gases in the atmosphere, including water vapor, methane, and all the CO2 that’s already there. All these gases absorb IR at different altitudes and at different frequencies, some of which overlap.

Wikipedia says that the present concentration of CO2 has a radiative forcing of 1.5W/m2. Right now the CO2 concentration in the atmosphere is 380ppm. Back in 1980 it was 340ppm. Although the forcing isn’t a linear function of concentration, it’s probably close to linear over a small interval, so it should be fair to say that the annual increase in forcing in a given year is [(2006-1980)/(380-340)]*(1.5/380). That equals .0026W/m2 per year. Assuming that’s a day and night average, and using 5.2*1014m2 for the surface area, we get 1.35*1012 (1.35 terawatt) increase (per year) of excess power added by CO2. For every year that I drive, I have to reflect my share of that 1.35TW back to space, along with all the 1.35TW fractional shares from previous years as well, or 1.9MWh the first year, 3.8 the next, etc.

Two conclusions: First, if I decide to remediate the CO2 I may eventually run out of driveway and perhaps I will have to move. Second, one shouldn’t ignore the annual contribution of energy from fuel burning since it is the equivalent of several years of CO2 emission, even if it’s far less than the CO2 cumulative contribution. If anything, this would seem to be a splendid argument for being less profligate regardless of our energy source.

My Tom Sawyer Moment

If you have read this far, you may well have come to the conclusion that I’m a climate nut, übergreenie, environmentalist, or someone who embodies great and perhaps excessive angst over the environment, global warming, and, for all I know, beryllium dust from nuclear fission weapons. I am none of the above. In fact, this article, with its interesting and, I hope, arithmetically-reasonable conclusion, was engendered only by the question first posed: “How big a mirror?” But if you wonder why there is so much argument and conflict on the issue of global warming, just take a close look at the error bars in the enlarged “Radiative Forcing Components” chart.

As far as painting the driveway is concerned, I’m not going to do it.

And there’s a simple, practical reason:

If the driveway is black, the snow melts faster. I’m hoping that by showing how cheap white striping paint can be, somebody elsewill paint his own driveway. Preferably someone in the South, where even more energy will be reflected, and where he won’t have to deal with snow that refuses to melt as a consequence.

☞ “But Richard,” I asked, my albedo strangely aroused by his analysis, “once the snow is on the driveway, the driveway is WHITE. No?”

No! [he responded] I can tell you’ve never tended a driveway during a northern winter. Of course you are correct if a major snow has JUST fallen. But you don’t leave it there, you shovel away (or person the snowblower) until the top layer is off to the side. At this point, depending on any number of pre- and post-snowfall weather conditions, you can be left with anything from an almost dry and completely usable driveway to an impenetrable layer of ice. In turn, the ice may be verging on transparent with the blacktop tantalizingly visible beneath, or it may be mottled and chunky. In any case, the ice is difficult to remove.

If transparent, the black driveway underneath will absorb enough sunlight to make a thin liquid layer under the ice, which turns shoveling from a frustrating experience to a pleasant session with the MP3 player. If the ice is less cooperative, you can still make enormous progress by chipping away a few areas and letting the sunlight melt the margins. This requires numerous trips to the driveway, but progress is much more rapid.

Given the variability of the wind, insolation, temperature, humidity, etc., it’s difficult to know in advance when the sun will help or be irrelevant. But – “trust me” – it’s a big help often enough that I’m willing to sacrifice a nanodegree of warming (or not-cooling) to have that advantage. If my driveway were flat, I might feel otherwise, but I live in hill country and the driveway with its few degrees of tilt occasionally traps even the 4WD Ford Escape (hybrid, of course). The Prius? Forget it!